Wave-equation based wave-field continuation statics technique and its application

2014 ◽  
Author(s):  
Han Zhanyi ◽  
Liu Liping* ◽  
Shang Xinmin ◽  
Hu Xiaoting ◽  
Pan Shunlin
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Field Continuation

Vertical seismic profile migration using the Kirchhoff integral

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 786-799 ◽  
Author(s):  
P. B. Dillon
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Near Field ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Processing Strategies ◽  
Receiver Array ◽  
Vsp Data ◽  
Kirchhoff Integral

Wave‐equation migration can form an accurate image of the subsurface from suitable VSP data. The image’s extent and resolution are determined by the receiver array dimensions and the source location(s). Experiments with synthetic and real data show that the region of reliable image extent is defined by the specular “zone of illumination.” Migration is achieved through wave‐field extrapolation, subject to an imaging procedure. Wave‐field extrapolation is based upon the scalar wave equation and, for VSP data, is conveniently handled by the Kirchhoff integral. The migration of VSP data calls for imaging very close to the borehole, as well as imaging in the far field. This dual requirement is met by retaining the near‐field term of the integral. The complete integral solution is readily controlled by various weighting devices and processing strategies, whose worth is demonstrated on real and synthetic data.

Path-linking interpretation of Kirchhoff diffraction

1995 ◽  
Vol 450 (1938) ◽  
pp. 51-65 ◽  
Keyword(s):  
Exact Solution ◽  
Wave Equation ◽  
Wave Field ◽  
Diffraction Field ◽  
Scalar Wave ◽  
Wave Fields ◽  
Linking Number ◽  
Diffraction Integral ◽  
Pass Through ◽  
Kirchhoff Diffraction Integral

The Kirchhoff-diffraction integral is often used to describe the (scalar) wave field from a monochromatic point source in the presence of ‘opaque’ screens. Despite criticisms that can be made of its ‘derivation’, the Kirchhoff field is an exact solution of the wave equation, and exactly obeys definite, though unusual, boundary conditions (Kottler 1923, 1965). Here, the path-integral picture of wave fields is used to interpret the Kirchhoff-diffraction field in terms of all conceivable propagation paths, whether or not they pass through the opaque screens. Specifically, it is noted that the Kirchhoff field equals Ʃ(1 ─ m )ψ m , where the sum is over all integers m , and ψ m is the wave field due to all paths from the source to the field point for which the number of outward screen crossings minus the number of backwards screen crossings is m . Expressed more topologically, m is the total linking number of a path, when closed by any unobstructed path, with the screen edge lines. Other models of diffraction by screens are compared with Kirchhoff diffraction in the path interpretation.

The application of wave field continuation for seismic refraction

1992 ◽  
Vol 5 (1) ◽  
pp. 67-78
Author(s):  
Lijun Wu ◽  
Rui Feng ◽  
Zhiming Huang
Keyword(s):  
Wave Field ◽  
Seismic Refraction ◽  
Field Continuation

scholarly journals Application of wave field continuation to the inversion of refraction data

1982 ◽  
Vol 87 (B2) ◽  
pp. 927-935 ◽  
Author(s):  
George A. McMechan ◽  
Robert W. Clayton ◽  
Walter D. Mooney
Keyword(s):  
Wave Field ◽  
Refraction Data ◽  
Field Continuation

scholarly journals Second-Order Time-Dependent Mild-Slope Equation for Wave Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Ching-Piao Tsai ◽  
Hong-Bin Chen ◽  
John R. C. Hsu
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Surf Zone ◽  
Linear Time ◽  
Second Order ◽  
Time Dependent ◽  
Wave Transformation ◽  
Stokes Wave ◽  
Perturbation Scheme ◽  
Mild Slope Equation

This study is to propose a wave model with both wave dispersivity and nonlinearity for the wave field without water depth restriction. A narrow-banded sea state centred around a certain dominant wave frequency is considered for applications in coastal engineering. A system of fully nonlinear governing equations is first derived by depth integration of the incompressible Navier-Stokes equation in conservative form. A set of second-order nonlinear time-dependent mild-slope equations is then developed by a perturbation scheme. The present nonlinear equations can be simplified to the linear time-dependent mild-slope equation, nonlinear long wave equation, and traditional Boussinesq wave equation, respectively. A finite volume method with the fourth-order Adams-Moulton predictor-corrector numerical scheme is adopted to directly compute the wave transformation. The validity of the present model is demonstrated by the simulation of the Stokes wave, cnoidal wave, and solitary wave on uniform depth, nonlinear wave shoaling on a sloping beach, and wave propagation over an elliptic shoal. The nearshore wave transformation across the surf zone is simulated for 1D wave on a uniform slope and on a composite bar profile and 2D wave field around a jetty. These computed wave height distributions show very good agreement with the experimental results available.

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